Question

How many terms of the AP :-9,-6,-3,.....must be taken so that their sum is 66?

Answer 1

The answer is in the sheet as shown above...

Answer 2

First term or a = - 9
Common difference or d = - 6 - ( -9 ) = - 6 + 9 = 3.
Sn = 66
Sn = n/2 ( 2a + (n - 1) *d )
66 = n/2 ( 2 * ( - 9 ) + ( n - 1 ) * 3 )
132 = n ( - 18 + 3n - 3 )
132 = n ( 3n - 21 )
132 = 3n^2 - 21n
3n^2 - 21n - 132 = 0
3n^2 + 33n - 12n - 132 = 0
3n ( n + 11 ) - 12 ( n + 11 ) = 0
( 3n - 12 ) ( n + 11 ) =0
n = 11 or 4
Now check which value is right
n = 11
66 = 11 / 2 ( 2 ( - 9) + 10 * 3 )
66 = 11/2 ( - 18 + 30 )
66 = 11/2 (12)
66 = 66
n = 11 it satisfy.
Now n = 4
66 = 4/2 ( 2 ( - 9) + 3 *3 )
66 = 2 ( - 18 + 9 )
66 = 2 * ( - 9 )
66 is not equal to - 18
n = 4 it does not satisfy.
11 terms are needed.
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